This is called the passive causative, used when someone else does work for you. The main verb is in the third/past participle form, and you add "got" or "had" for past tense (or "will get/will have" for future tense). Examples: "John drove his car across the country" (This means John did the driving himself); "John had his car driven across the country" (This means someone else drove John's car, and maybe John took a plane); "She got her dress cleaned and pressed" (perhaps at the dry cleaners); "The prime minister will have his memoirs written when he leaves office" (This means another person will write the PM's memoirs in the future)

cut is a strange word in that it doesn't change tense in these types of sentences, The context/other words tells you the tense, in your sentence it is past tense, because you have had ( past tense) it cut. But I can also say, Tomorrow I will get my hair cut. so here it is in future tense....I'm at the hairdressers getting my hair cut..present tense. It would change tense if you were the person doing the cutting though ie: I cut his hair- past tense, I am cutting his hair-present tense I would try not to worry about getting your head round causative verb form...I'm English and I don't even know what that means. lol. Learning a language should be about doing, and learning by context etc, leave the fancy grammar terms to the professional linguists, you will only get confused! Just like I was by the first part Brad's answer, no offence Brad, Im sure what you said is correct and true, I just think its better to try and keep things simple!

Try other ones and you'll see: Have me posted, get you confused. Keep you informed. The "past participle", and yes, usually only "get", "have" and "keep" can be applied to the structure; I wouldn't suggest you learn "causatives", what Mr. C brings up below; it's rather a big and complicated term.